14.多元线性回归

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets

获取数据

boston = datasets.load_boston()
X = boston.data
y = boston.target

数据处理

X = X[y < 50.0]
y = y[y < 50.0]

数据分割

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)

多元线性回归方程θ参数求解

from sklearn.linear_model import LinearRegression
lin_reg = LinearRegression()
lin_reg.fit(X_train, y_train)

θ参数

lin_reg.coef_

array([-1.15625837e-01,  3.13179564e-02, -4.35662825e-02, -9.73281610e-02,
       -1.09500653e+01,  3.49898935e+00, -1.41780625e-02, -1.06249020e+00,
        2.46031503e-01, -1.23291876e-02, -8.79440522e-01,  8.31653623e-03,
       -3.98593455e-01])

θ截距

lin_reg.intercept_

32.59756158869991

预测结果 R2

lin_reg.score(X_test, y_test)

0.8009390227581037

kNN Regressor 线性回归

from sklearn.neighbors import KNeighborsRegressor

knn_reg = KNeighborsRegressor()
knn_reg.fit(X_train, y_train)
knn_reg.score(X_test, y_test)

0.602674505080953

网格搜索超参数

from sklearn.model_selection import GridSearchCV

param_grid = [
    {
        "weights":["uniform"],
        "n_neighbors":[i for i in range(1, 11)]
    },
    {
        "weights":["distance"],
        "n_neighbors":[i for i in range(1, 11)],
        "p":[i for i in range(1, 6)]
    }
]

knn_reg = KNeighborsRegressor()
grid_search = GridSearchCV(knn_reg, param_grid, n_jobs=-1, verbose=1)
grid_search.fit(X_train, y_train)

Fitting 5 folds for each of 60 candidates, totalling 300 fits

 

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done  34 tasks      | elapsed:    1.2s
[Parallel(n_jobs=-1)]: Done 300 out of 300 | elapsed:    1.4s finished

Out[34]:

GridSearchCV(cv=None, error_score=nan,
             estimator=KNeighborsRegressor(algorithm='auto', leaf_size=30,
                                           metric='minkowski',
                                           metric_params=None, n_jobs=None,
                                           n_neighbors=5, p=2,
                                           weights='uniform'),
             iid='deprecated', n_jobs=-1,
             param_grid=[{'n_neighbors': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
                          'weights': ['uniform']},
                         {'n_neighbors': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
                          'p': [1, 2, 3, 4, 5], 'weights': ['distance']}],
             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,
             scoring=None, verbose=1)

grid_search.best_params_

{'n_neighbors': 6, 'p': 1, 'weights': 'distance'}

grid_search.best_score_

0.6243135119018297

grid_search.best_estimator_.score(X_test, y_test)

0.7353138117643773